1. Stability Stratification, Buoyancy and Weather Flashcards
What is stability?
Densest fluid is at the bottom, below the next densest, with the least dense fluid at the top (d.rho/dy < 0)
What is the ideal gas law?
Pv = RT/M (where v is 1/rho)
In a gravitational field, what can be said about pressure with respect to y?
dp/dy = -g x rho
Derive an equation relating pressure to temperature in an adiabatic environment
(T1/T0) = (P1/P0) ^(n-1/n)
Derive the adiabatic lapse rate of air
[hint h0 = P0 V0/g]
[hint: P0^(n-1/n) = C^(n-1/n) x rho0^(n-1)]
Final solution is dT/dy = - (T0/h0)(n-1/n)
Approximately -10 degrees/km
Define a stable atmosphere
A pertubation is damped out (density decreases with increasing height, d.rho/dy < 0)
Define a neutrally stable atmosphere
A pertubation affects the system but is not amplified (density remains constant with increasing height, d.rho/dy =0
Define an unstable atmosphere
A pertubation is amplified and results in significant changes to the system (density increases with increasing height, d.rho/dy > 0)
Draw and label the adiabatic lapse rate of air with an unstable ELR and a stable ELR
stable is steeper than ALR
unstable is shallower than ALR
Explain how temperature pumping occurs over mountains, you may draw a diagram
Humid air rises at the ALR (A to B)
As the vapour starts to condense (point B), the air heats up (due to its’ latent heat) and so rises (B to C) at a lower humid adiabatic lapse rate (e.g. 5c/km)
At the top of the mountain (point C) as the vapour condenses, some rain falls.
On the other side of the mountain (C to D), the air falls at the humid ALR, water droplets evaporate and you get mist until all water has evaporated off (point D)
Then the air falls at the ALR (D to E).
Given some water was lost as rain, Point D is higher than point B and so the final temp can be considerably higher than original.
Explain why there is very little mixing in evenings
Radiative losses in the evening lead to the earth cooling. This results in the air at lower altitudes being considerably lower than that higher up. This is a very stable atmospheric condition ( cold air is denser) and can even lead to inversion ( where temp increases with height).
Explain how mixing occurs in mornings
As the sun rises, it heats the earth resulting in hotter air at lower altitudes. This is very unstable as the hot air is less dense and so wants to rise. For conservation cooler air must fall to replace this warm air, resulting in mixing.
What is the Brunt vaisala frequncy?
A balloon in a stratified liquid will oscillate because the density of fluid in the balloon is constant, while the density of surrounding air varies with height.
The balloon will rise/fall to where its density equals that of its surroundings (oscillating at the Brunt vaisala freq).
Define the volumetric expansion coefficient. What does this tell us about the density (rho_e) at a given temperature (T) ?
B = -1/rho x d(rho)/dT rho_e = rho_0[1-B(T-T0)]
Derive the Brunt Vaisala Frequency
Aiming for:
d2y/dt2 = -(gB[dt/dy])y
has solution y = sin(wt) with w = SQRT(gB[dt/dy])
